Advertisements
Advertisements
Question
If the volume of a cuboid is 3x2 − 27, then its possible dimensions are
Options
3, x2, − 27x
3, x − 3, x + 3
3, x2, 27x
3, 3, 3
Advertisements
Solution
We have to find the possible dimension of cuboid
Given: volume of cuboid `3x^2 - 27`
`3x^2 -27 = 3x^2 - 3xx 3 xx 3`
` = 3x^2 - 3 xx 3 xx 3`
Take 3 as common factor
`3x^2 - 27 = 3(x^2 - 3^2)`
Using identity `x^2 -y^2 = (x+y)(x-y)`
We get,
`3x^2 - 27 =3(3x+3) (x-3)`
Here the dimension of cuboid is 3,3, x + 3, x - 3
APPEARS IN
RELATED QUESTIONS
Evaluate the following product without multiplying directly:
95 × 96
Write the following cube in expanded form:
`[x-2/3y]^3`
Give possible expression for the length and breadth of the following rectangle, in which their area is given:
| Area : 35y2 + 13y – 12 |
What are the possible expressions for the dimensions of the cuboids whose volume is given below?
| Volume : 12ky2 + 8ky – 20k |
If \[x - \frac{1}{x} = - 1\] find the value of \[x^2 + \frac{1}{x^2}\]
Simplify of the following:
If a + b + c = 9 and ab + bc + ca = 23, then a2 + b2 + c2 =
The difference between two positive numbers is 5 and the sum of their squares is 73. Find the product of these numbers.
If 3x + 4y = 16 and xy = 4, find the value of 9x2 + 16y2.
Use the direct method to evaluate :
(2a+3) (2a−3)
Evaluate: 20.8 × 19.2
Expand the following:
(m + 8) (m - 7)
Expand the following:
(x - 3y - 2z)2
Find the squares of the following:
`(7x)/(9y) - (9y)/(7x)`
Simplify by using formula :
(x + y - 3) (x + y + 3)
If m - n = 0.9 and mn = 0.36, find:
m2 - n2.
If x + y = 1 and xy = -12; find:
x - y
Simplify:
(7a +5b)2 - (7a - 5b)2
Prove that (a + b + c)3 – a3 – b3 – c3 = 3(a + b)(b + c)(c + a).
